Reference dependent preferences incontests and non cognitive ability in the labour market

Reference-Dependent Preferences in Contests and Non-Cognitive Ability in the Labour Market Inaugural-Dissertation zur Erlangung des Grades eines Doktors der Wirtschafts- und Gesellschaftswissenschaften durch die Rechts- und Staatswissenschaftliche Fakult¨ at der Rheinischen Friedrich-Wilhelms-Universit¨ at Bonn vorgelegt von Jan Niklas Bergerhoff aus Herne Bonn 2015 Angefertigt mit Genehmigung der Rechts- und Staatswissenschaftlichen Fakult¨at der Rheinischen Friedrich-Wilhelms-Universit¨at Bonn Dekan: Prof Dr Rainer H¨ uttemann Erstreferent: Prof Dr Sebastian Kube Zweitreferent: Prof Dr Matthias Kr¨akel Tag der m¨ undlichen Pr¨ ufung: 21 September 2015 Erscheinungsjahr: 2015 Abstract The dissertation includes four individual essays that are laid out over four separate chapters Following a short overall introduction in Chapter 1, Chapter models the strategic interaction between two agents who engage in a game-theoretical contest and hold expectation-based reference-dependent preferences We show, that agents who find themselves disadvantaged ex ante, in this setting end up as favourites in two out of three possible equilibria In Chapter we investigate, using field data, whether it is possible to invest in non-cognitive ability through an educational policy We measure the impact of a study abroad experience on non-cognitive skills and compute its monetary implications using wage data from the German Socio-Economic Panel The project presented in Chapter is an outcome of initiating the study series Fachkraft 2020 which is, at the moment of writing, the biggest student survey in Germany with more than 40,000 annual participants Based on about 23,000 student responses we examine whether there is selection and change of non-cognitive abilities in different study tracks of German higher education We find sizeable selection, but little change Lastly, Chapter models the impact of the internationalisation of higher education on economic growth in a two country setting We provide conditions necessary for internationalisation to be beneficent and simulate different growth paths for both countries Parts of this thesis have been published in the following articles: • Bergerhoff, Borghans, Seegers, and van Veen (2013) • Bergerhoff and Vosen (2015) (working paper) f¨ ur meine Mutter Acknowledgements Locus of Control, one of the personality measures we use, describes how much you think that what you experience is the result of your own making and to what extend it depends on the decision of other people While I believe to have some control, I am in no way blind to the enormous support I have received from many great people over the years I would like to thank my supervisors Sebastian Kube and Matthias Kr¨akel Both have given me the freedom to explore and develop my own ideas I would like to thank Sebastian Kube for believing in the idea behind Chapter when there was still controversy about the feasibility of the project This initial trust was an important foundation that contributed the necessary serenity to explore ideas I would like to thank Mathias Kr¨akel for his excellent supervision of Chapter His kind support and all his comments and ideas during our project were incredibly helpful for us, and his speed and attention to detail never failed to impress me Great thanks goes to my co-author Philipp Seegers who has accompanied me all the way starting from the bachelor programme in Maastricht and who I really value as a friend Working with him has always been a great pleasure and I am sure we will keep working together in the future I would also like to thank my other co-author Agnes Vosen who went with me through the natural ups and downs of challenging proofs I owe a great debt to Lex Borghans, who is also a co-author, but was in effect really my third supervisor His feedback and ideas have greatly benefited Chapters 3, and and I am very grateful to him that he always treated me like one of his own students I would like to thank Tom van Veen for encouraging Philipp and me to think about the internationalisation of education and for organising our participation at the 67th IIPF congress I am also very grateful to Pia Pinger for her great feedback and for supporting the Fachkraft 2020 team I was lucky to have great colleagues Especially, thank you Linda, Nazar, Adrian and Tobit for the many discussions, coffees and good company Moreover, it is of special importance to me to thank Stephan Hartmann for warmly welcoming me on the Fachkraft 2020 team and for all the good time and communal work we have achieved since i It is likely that I would have never have begun this dissertation had it not been for Roy Allen, Martin Frayn and Stephen Holroyd It was them who shared their intrinsic passion to study economics and history with me, first when I was their student, and later as a friend I would like to thank the Bonn Graduate School of Economics for its financial support during my Ph.D and the Friedrich-Ebert-Stiftung for their support leading up to it But out of all people I am most indebted to my parents, who have loved and supported me all my life I would like to thank my mother, especially, for having had the courage to send me off to school in England and for making my entire educational path possible Last, but certainly not least, thank you Sebastian for all the wonderful dinners, our great time together, and for insisting that Star Trek is an essential part of every Ph.D., not only in Physics ii Contents Introduction Can being behind get you ahead? 2.1 Abstract 2.2 Introduction 2.3 The Model 11 2.4 2.3.1 Utility with reference-dependent preferences 11 2.3.2 Endogenous Reference Points 13 Multiple Equilibria 19 2.4.1 Confirming Asymmetric Equilibria 19 2.4.2 Type One Turn Around Equilibria 20 2.4.3 Type Two Turn Around Equilibria 22 2.4.4 Unique Turn Around Equilibria 24 2.4.5 Catching Up Equilibria 25 2.5 Conclusion 27 2.6 Appendix 28 2.7 2.6.1 Proof of Proposition 1: 30 2.6.2 Proof of Proposition 2: 31 2.6.3 Proof of Proposition 3: 33 2.6.4 Proof of Proposition 4: 41 2.6.5 Proof of Proposition 5: 42 Technicalities 43 2.7.1 Derivation of (2.11) and (2.12) in Lemma 43 2.7.2 Derivation of (2.13) in Lemma 43 iii 2.7.3 Derivation of (2.14) in Lemma 44 Investing in Personality? 47 3.1 Abstract 47 3.2 Introduction 48 3.3 Personality Measures 51 3.4 Data 53 3.5 Results 54 3.6 The size of the effect 59 3.7 Conclusion 63 3.8 Appendix 65 3.8.1 Locus of Control Statements 65 Personality and Field of Study 71 4.1 Abstract 71 4.2 Introduction 71 4.3 Data 74 4.4 Methodology 75 4.5 Results 77 4.6 4.5.1 Selection and Mean Level Change 77 4.5.2 Personality Profiles 79 4.5.3 Change in Dispersion 83 Conclusion 85 International Education and Economic Growth 87 5.1 Abstract 87 5.2 Introduction 87 5.3 The Model 90 5.4 5.3.1 Basic equations 90 5.3.2 Solution 92 5.3.3 The Effects of International Education 93 Empirics 96 5.4.1 Parameter Callibration 96 iv 98 International Education and Economic Growth This condition is always met if ρ < φ Moreover, we can see that in the long run, when migration is balanced, the growth rate increases with the productivity of education of domestic students in the foreign country A certain share of these students returns to Home after graduation Additionally, Home benefits by the international premium that Home students in Foreign gain This effect increases if more foreign students decide to stay in Home after education Finally, we can have a look at the level effects in the case where student migration balances s(1 − u − uθ) 1−α α λ < s − u − uθ(1 − i + ∗ i) λ 1−α α ; ⇒λ < λ∗ This means that if student flows balance the level effect is no longer dependent on the actual student inflow but on the probability that those students stay in the country If the probability that home students stay abroad is smaller than the probability that foreign students stay in Home, the level effect is positive in the home country 5.4 5.4.1 Empirics Parameter Callibration In order to apply the model it is essential to evaluate its parameters empirically The exact share of international students depends on the country at hand Within the model the internationalisation rate i is measured in terms of the share of students which are educated in a foreign country A broad comparison of those rates of internationalisation is possible with the help of a yearly assessment by Eurostat According to their measurement, internationalisation within Europe averages 2.9 percent (Statistical Office of the European Communities, 2012) However, given that not all international students register in the foreign country, the Eurostat figures are likely to be under-reported This becomes visible at the example of the Netherlands, for which Nuffic collects data on a university level While Eurostat reports that 2.3 percent of the Dutch students go abroad, Nuffic (2011) reports a rate of internationalisation of 7.1 percent Since the Netherlands are below the European average in terms of outgoing students in (Statistical Office of the European Communities, 2012), the simulations are done for international shares between and 10 percent 99 5.4 Empirics Data quality is weaker when it comes to the probability to stay in a foreign country after graduation In a recent paper, Bijwaard (2010) suggests that male study related migrants have a chance of 19 percent to stay in the Netherlands For female students the chance is estimated at 26 percent The values fluctuate strongly between different countries of origin Moreover, these figures might be over reported The data includes only students who register in the Netherlands and these have a higher probability to stay than students which not even register in the first place Hence, the probability to stay used in the simulations is somewhat lower and equal to 15 percent To estimate the share of students in the labour force as measured by the model we consider the working population only Eurostat data shows that men in Europe work between 40 and 46 years over their lifetime, while women work 36 to 44 years (Brugiavini & Peracchi, 2005) Moreover, university education is supposed to require three to four years for a Bachelor and four to six years for a Master degree In reality even more time may be needed to finish university Combining this information with the European target that 40 percent of the population should hold a university degree allows to calculate scores for the population share of students These range between roughly 2.5 percent and 7.5 percent, and hence, percent will be used in the simulations Values for the teacher to student ratio θ can be found on the basis of data published by the European Commission Currently, there is a total of roughly 19 million students in Europe, while higher education institutions employ 1.5 million staff members Hence, θ should be close to percent This number neglects workers that work on buildings and equipment for the university sector Suppose there was no international education Setting i = i∗ = 0, the human capital accumulation equation would reduce to h˙ = huρ as in the original Lucas model The parameter ρ, then, represents the growth of the human capital stock In a sense, it is the return on human capital for every unit of human capital each time period To evaluate plausible values for ρ we make use of the vast literature estimating real returns to education In their influential review paper, Psacharopoulos and Patrinos (2004) estimate the social return on investments into education to be 10.8 percent In the context of our model every unit invested in human capital grows with rate ρ and every one percent increase in human capital results in a (1 − α) percent increase in output To obtain an estimate for ρ we hence use that redu ≈ ρ(1 − α) Setting redu = 10.8 and α = 13 gives an estimate for ρ at 15.75 percent The return in human capital that is specific to international education is given 100 International Education and Economic Growth by This variable is important as it determines the extra learning gains from international education Unfortunately, not much conclusive evidence exists on whether international education holds a return premium However, several empirical studies have shown that students spending time abroad have benefited in terms of improved language skills and better cultural understanding (Sutton & Rubin, 2004; Freed, 1995) Many verbal accounts, moreover, suggest that students undergo some personal development when going abroad International experience, indeed, catches a wage premium in the labour market, but currently it is uncertain how much of it is attributable to selection (Oosterbeek & Webbink, 2006) Applying the same approximation as above = 0.02 implies a rate of return premium of about 1.3 percent 5.4.2 Simulations The model as formulated can be calibrated to fit many different pairs of countries Whenever we compare our findings to an economy with purely domestic higher education, we name this economy “‘Lucas”’ Whenever we this, we mean that we are comparing our results to the simplified version of the Lucas model rather than with the original In the following section we will consider a pair that has the same parameter values except for size, where we assume that the labour force of the foreign country is initially four times larger This setup roughly resembles the cases of Germany and the Netherlands All parameter values used lie within the ranges established in the previous section: Model Parameter Value α s, δ θ u i ρ, λ 0.1 0.08 0.05 0.1 0.15 Table 5.1: Parameter values used for callibration Imagine this two-country world and suppose that international education does not carry any premium Given that all parameters are identical with the exception of population size, we should expect to see a great surplus of students entering the small country every period of time Since all students have the same probability to stay, the small country then faces a positive migration of well-qualified students as compensation for the initial increase in the cost of education Figure 5.1 plots the development of both countries’ income per capita relative to what it would have been without international education The left panel assumes that the population size of both countries 5.4 Empirics 101 remains the same, and thus that student migration is offset by exogenous factors The small country represented by the thick line initially starts off at a lower income per capita level This decrease in GDP per capita equals −0.084 percent However, since it enjoys a larger growth rate, it reaches the no-internationalisation level of income within only four periods Thereafter, brain gain leads to constantly higher levels of income than under the noninternational Lucas regime and to 0.034 percent faster growth in steady state Table 5.2 gives additional comparative statics for this scenario relative to the domestic education economy, which, under our parameters for u and ρ, grows at 0.75 percent in steady state If more students of the home country study abroad (i = 0.15) the extra steady state GDP-growth decreases When the mobility of foreign students increases (i∗ = 0.15) the steady state growth rate increases A simultaneous increase in both mobility rates is more advantageous for the smaller than for the larger country The same is true for the percentage students that stay in the country of study An increase of the fraction of students that remain abroad negatively influences the growth rate, but the smaller country benefits more from a higher percentage of stayers than the larger country The right panel of Figure shows what happens if the population size of both countries starts to change due to student mobility Since for the Home country GDP growth is now accompanied by a population growth Home needs much more time to recover from its initial drop, and GDP per capita will grow slower The reason for this is that the capital stock only adjusts gradually to the increased population size If an increase in the number of workers would be accompanied by an extra investment in capital, the growth patterns would look more like in the first panel Figure shows what happens in the very long run With a constant increase in population the smaller country becomes larger and larger This means that the mobility flows become more equal The smaller country has more students and, therefore, also more students will study abroad Eventually, the differences in population size will disappear and the growth effects vanish It should be stressed that this result is a consequence of having constant and equal parameter values for u, i, λ and ρ If one country, for example, has a higher internationalisation rate, country sizes will not fully equalise in the long run Thus far, in the Figures we have only considered the purely distributional effects of international education Figure 5.3 repeats the simulation assuming an international premium of two percent corresponding to about 1.3 percent greater returns to education This corresponds to the penultimate row in table 5.2 Relative growth rates of both countries increase across scenarios such that in either scenario both countries benefit from international education Economic growth in the home country increases from 0.034 percentage points to 0.049 while for the foreign country a lower growth of −.0085 turn into a faster growth of 0.0044 Based on these parameters economic growth in the 102 International Education and Economic Growth smaller country would increase with 0.049 percentage points while GDP per capita would increase with 0.0044 percentage points The average annual extra growth in both country therefore equals 0.013 percentage points This shows that at the most plausible values of the parameters international education is beneficial for both countries Naturally, policy makers can attempt to increase their share of the overall gains, by targeting variables like the probability to stay through migration policy or by making it easier for foreign students to start studying Even if no international premium exists, international education may be mutually beneficial This is, for example, the case when one country has a higher productivity in educating students than the other country; a relationship we may see between a more and a less developed country Under the assumption that only students from the less developed country want to study and stay in the more developed country, international education is universally beneficial as shown in Figure 5.4 Here, the less developed country benefits as the higher human capital of the students returning from the developed country outweighs the human capital loss from brain drain The developed country loses in the short run due to the higher costs of education, but quickly recovers and gains from the inflow of talented students later on Ypc YpcLuc 1.020 Ypc YpcLuc 1.015 1.002 1.010 1.000 1.005 1.000 0.998 0.995 10 20 30 40 50 Time 0.996 10 20 30 40 50 Time Figure 5.1: Base Scenario without Labour Adjustments (Left), with Labour Adjustment (Right) 5.5 Conclusions In this paper we developed an endogenous growth model to investigate the effects of internationalisation in higher education on economic growth In aggregate, assuming that individual students only go abroad when that is beneficial to them, in the long run internationalisation is always beneficial for the two countries together The distribution of the gains, however, depends on a variety of parameters like the rate of internationalisation and the probability to stay in a foreign country While there are cases in which both countries gain, it is also possible that one country loses 103 5.5 Conclusions Rel to Lucas Base L exog i = 0.15 i∗ = 0.5 i = i∗ = 0.15 λ = 0.2 λ∗ = 0.2 λ = λ∗ = 0.2 ρ = ρ∗ = 0.2 ρ = ρ∗ = 0.1 = ∗ = 0.02 = ∗ = 0.05 Init ∆ (%) -0.084 -0.070 -0.141 -0.126 -0.085 -0.085 -0.085 -0.085 -0.085 -0.085 -0.085 NL Recov in (t) SS Gr.(%) 4.00 0.034 4.00 0.028 4.00 0.056 4.00 0.051 4.50 0.030 2.75 0.049 3.00 0.045 3.00 0.034 6.00 0.034 2.75 0.049 1.75 0.070 DE Init ∆ SS Gr 0.021 -0.0085 0.017 -0.0071 0.035 -0.014 0.032 -0.013 0.021 -0.0075 0.021 -0.012 0.021 -0.011 0.021 -0.0085 0.021 -0.0085 0.021 0.0044 0.021 0.014 Table 5.2: Comparative Statics for the left panel of Figure 5.1 The first column gives the Initial Change of Output per Capita relative to Lucas In the second column we give the time it needs to reach the Lucas’ level of output per capita again The third column has the changes in the steady state growth rate due to internationalisation in percentage points Ypc YpcLuc gh ghLuc 1.04 1.03 1.02 1.01 1.00 0.99 0.98 1.020 1.015 1.010 1.005 1.000 0.995 0.990 200 400 600 800 100012001400 Time 200 400 600 800 100012001400 Time Figure 5.2: Long Run adjustment of per Capita Income and Human Capital relative to Lucas when Labour is Endogenous Ypc YpcLuc 1.020 Ypc YpcLuc 1.010 1.008 1.006 1.004 1.002 1.000 0.998 1.015 1.010 1.005 1.000 0.995 10 20 30 40 50 Time 10 20 30 40 50 Time Figure 5.3: Scenario with ∗ = 0.02 without Labour Adjustments (Left), with Labour Adjustment (Right) 104 International Education and Economic Growth Ypc YpcLuc 1.020 Ypc YpcLuc 1.030 1.025 1.020 1.015 1.010 1.005 1.015 1.010 1.005 1.000 0.995 10 20 30 40 50 Time 10 20 30 40 50 Time Figure 5.4: Case where countries are unsymmetric in most parameters except size: ρ = 0.2, ρ∗ = 0.1; i = 0, i∗ = 0.2; λ∗ = 0.2 This implies that there can be two obstacles for the internationalisation of university education First, countries that emphasise short run effects in their decision making might try to limit access for foreign students The reason for this lies in the costs of education which lowers short term output Second, an unequal division of the benefits of internationalisation might hamper international cooperation When a large fraction of graduates leaves the country after studying there, net receiving countries may find it more difficult to benefit from international education At the opposite extreme, if a substantial fraction of the students stays in the country of study, it will be attractive for each individual country to promote foreign students to study in their country This could lead to a rat race in which countries attempt to get an as large as possible share of the flow of international students Considering long-term growth, a country benefits if it attracts many foreign students who stay in the country A policy to open up universities for foreign students is therefore complementary to a policy to make the labour market attractive for these foreign students 5.5 Conclusions 105 Concluding remarks All mistakes are my own 107 108 International Education and Economic Growth References Almlund, M., Duckworth, A L., Heckman, J J., & Kautz, T D (2011) Personality psychology and economics (Tech Rep.) 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Brussels, Belgium: European Commission Wallston, K A., Wallston, B S., & DeVellis, R (1978) Development of the multidimensional health locus of control (mhlc) scales Health Education & Behavior , (1), 160–170 Zimmermann, J., & Neyer, F J (2013) Do we become a different person when hitting the road? personality development of sojourners Journal of personality and social psychology, 105 (3), 515 [...]... slightly behind before the break compared to the leading team Instead of having a lower probability to win, the team being behind by one point is more likely to win the game In case of the NBA data the trailing team has 1.1 percentage points higher probability to win the game than the leading team For the NCAA the result is even stronger: 5.6 percentage points The difference in winning probability at the breakpoint... choose the same level of effort since both players have the same marginal costs and benefits are also the same due to the symmetry of the normal distribution’s density Therefore, the player ahead always maintains the same advantage in the relative winning probability An extra incentive rewarding more unequal winning probabilities like reference- dependent preferences, in this setting, would just widen the. .. means that independent of the interims feedback, both competitors invest the same level of effort and only the sum of efforts decreases the more uneven the feedback is Without any difference in effort provisions and the corresponding changes in the relative winning probabilities these tournaments are essentially decided by the initial unevenness and chance Providing information about the intermediate... exist Remarkably, in two of these classes the player being behind overtakes the opponent and ends up with a higher probability of winning the tournament In tournaments where the initial unevenness is strongly favourable for one party we find a unique equilibrium, in which the leading player extends the lead by investing more effort than the player behind However, when the game is tight and the tournament... result, such non- orthodox” preferences are, if they are, typically introduced to economic theory in isolation and one at a time An interesting class of non- standard motives are reference- dependent preferences The concept that received much attention following the article of K¨oszegi and Rabin (2006) reflects the empirical finding that one is particularly happy when an event exceeds expectations and particularly... that Player B is initially disadvantaged and considers investing more effort than Player A For Player A this could be an equilibrium since the player is willing to settle at a point where the marginal benefits together with the marginal reduction of the reference- dependence cost meets the marginal costs The key to understanding this intuition is to see that the incentive effect of reference- dependence... reference point as the derivative ∂r ∂eA 2.3.2 Endogenous Reference Points In the following we endogenise the reference points and employ the choiceacclimating personal equilibrium concept of K¨oszegi and Rabin (2006) to derive the player’s first and second order conditions After establishing a necessary and sufficient condition for the interiority of all solutions in Lemma 1, we show in Lemma 2 and Lemma 3... following incentive effect7 : 6 Like Gill and Stone (2010) we do not model a reference point in the effort domain We believe that further conceptual work on what a reference point in the effort domain could be is interesting and could yield a valuable addition to this and other models Yet with all its psychological and technical implications it exceeds the scope of this paper ∂R 7 The corresponding term... been described by Gill and Stone (2010) Note that the incentive does not point the player into a particular direction Whether the player “gets ahead” or “falls behind” is not important Evenness at the end of the period is unattractive for agents with reference points since it jointly maximises the size of the disutility from falling short of the reference point weighted by the probability of its occurrence... reference- dependence in the lower graph of Figure 2.1 is to steepen and drive apart both player’s marginal benefits The peak of the marginal benefits of both players is now located in the area where they themselves are more likely to win Intuitively, both players benefit most from their effort when they can use it not only to increase their own winning probability, but also to decrease the uncertainty ... Therefore, the player ahead always maintains the same advantage in the relative winning probability An extra incentive rewarding more unequal winning probabilities like reference- dependent preferences, ... behind before the break compared to the leading team Instead of having a lower probability to win, the team being behind by one point is more likely to win the game In case of the NBA data the. .. point where the marginal benefits together with the marginal reduction of the reference- dependence cost meets the marginal costs The key to understanding this intuition is to see that the incentive